Ronald Koeman fielded a strong Southampton team - the likely side to face Vitesse next Thursday - as Southampton entered De Kuip to take on his, and Pellè and Clasie's former employers.
Maarten Stekelenburg started in goal, while new signings Cédric and Clasie both started, with Cuco Martina and Juanmi starting from the bench.
Saints could've stormed into an early lead when a burst of energy from Sadio Mané saw the Senegalese forward put the ball on a plate for Pellè, only for the Southampton frontman to blaze over from close range.
Dirk Kuyt then offered a rare threat at the other end of the pitch, when he nodded just over Stekelenburg's bar from close range.
Up until the 41st minute, there had been just one shot on target, but Pellè changed that when he profited from some smart play from Dušan Tadić.
A direct ball down the flank from Matt Targett found the Serbian playmaker, who drew Kenneth Vermeer from his goal-line before sliding the ball across for Pellè to knock the ball over the line.
Rick Karsdrop fizzed an effort over the bar of the Saints goal from 25-yards, as the Rotterdammers started the second half in more impressive fashion than Koeman's men.
In the 61st minute, Koeman swapped James Ward-Prowse and Juanmi for Mané and Clasie, who departed to an emotional standing ovation.
In the minute that followed the substitution, Saints doubled their lead when Yoshida headed home from a deep free-kick served up by Steven Davis.
Juanmi presented a chance to Jens Toornstra when a slack pass found its way to the Feyenoord man, only for the Dutch midfielder to curl an effort off the outside of the post.
Dušan Tadić was replaced in the 75th minute by Harrison Reed, before Graziano Pellè received a standing ovation of his own when he made way for Shane Long.
Long proved pivotal to Juanmi adding the third goal of the evening, the Irishman plucking captain José Fonte's long pass out of the air before playing in Juanmi, who took one touch before burying his low drive.
Southampton will return to action next Thursday, when Vitesse Arnhem visit St. Mary's in the first leg of the Europa League third round.
Southampton XI: Stekelenburg; Cédric, Fonte, Yoshida, Targett; Wanyama, Clasie (Ward-Prowse - 61'); Mané (Juanmi - 61'), S. Davis, Tadić (Reed - 75'); Pellè (Long - 82').
Unused Substitutes: K. Davis, Martina, McCarthy, Stephens, Debayo, Rodriguez.